Langevin equation

From CFD-Wiki

The stochastic differential equation (SDE) for velocity component ,
the Langevin equation is

where is a Wiener process.
is the turbulence intensity and a Lagrangian time-scale.

Th finite difference approximation of the above equation is

where is a standardized Gaussian random variable with 0 mean an unity variance
which is independent of on all other time steps (Pope 1994).
The Wiener process can be understood as Gaussian random variable with 0 mean
and variance